CENTER OF MASS AND MOMENT OF INERTIA 1< 2. Find the center of mass of a right circular cone whose densi varies inversely as the square of the distance from the apex, the distan being measured along the axis. dm = r • iry2 • dx = ^'7T Tlira •dx where n is the density at a unit distance from the apex. Therefore 1 ~h • ( xdx n h'2 h '' 2 • f dx •S n FIG. 82. PROBLEMS. 1. Find the center of mass of a right circular cone, the density of whi varies inversely as the distance from the vertex. 2. Find the center of mass of a circular plate, the density of whi varies as the distance from a point on the circumference. 3. Find the center of mass of a cylinder, the density of which var with the nth power of the distance from one base. 4. Find the center of mass of a quadrant of an ellipsoid. 6. Find the center of mass of a hemisphere, the density of which var as the distance from the center. 119. Center of Mass of a Number of Bodies. — Let mi; w etc., be the masses and Xi, x2, etc., be the ^-coordinates of ti centers of mass of the individual bodies. Then if x denot the re-coordinate of the center of mass of the entire syste we can write xdm